Problem: Simplify the following expression: $z = \dfrac{63a + 63}{-35a}$ You can assume $a \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $63a + 63 = (3\cdot3\cdot7 \cdot a) + (3\cdot3\cdot7)$ The denominator can be factored: $-35a = - (5\cdot7 \cdot a)$ The greatest common factor of all the terms is $7$ Factoring out $7$ gives us: $z = \dfrac{(7)(9a + 9)}{(7)(-5a)}$ Dividing both the numerator and denominator by $7$ gives: $z = \dfrac{9a + 9}{-5a}$